Inverse problem: Reconstruction of modified gravity action in Palatini formalism by Supernova Type Ia data

Abstract

We introduce in $f(R)$ gravity--Palatini formalism the method of inverse problem to extract the action from the expansion history of the universe. First, we use an ansatz for the scale factor and apply the inverse method to derive an appropriate action for the gravity. In the second step we use the Supernova Type Ia data set from the Union sample and obtain a smoothed function for the Hubble parameter up to the redshift~1.7. We apply the smoothed Hubble parameter in the inverse approach and reconstruct the corresponding action in $f(R)$ gravity. In the next step we investigate the viability of reconstruction method, doing a Monte-Carlo simulation we generate synthetic SNIa data with the quality of union sample and show that roughly more than 1500 SNIa data is essential to reconstruct correct action. Finally with the enough SNIa data, we propose two diagnosis in order to distinguish between the $\Lambda$CDM model and an alternative theory for the acceleration of the universe.

8 pages, 8 figures, accepted in Phys. Rev. D

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Cited by in corpus (15)

• f(R) theories
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Kinematic model-independent reconstruction of Palatini $f(R)$ cosmology
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Testing f(R) gravity with the simulated data of gravitational waves from the Einstein Telescope
• Reconstructing cosmic acceleration from modified and non-minimal gravity: The Yang-Mills case
• Loop Quantum Cosmology Matter Bounce Reconstruction from $F(R)$ Gravity Using an Auxiliary Field
• Vacuum Solution of a Linear Red-Shift Based Correction in $f(R)$ Gravity
• Structure formation in $f(R)$ gravity: A distinguishing probe between the dark energy and modified gravity
• Conformal Transformations in Metric-Affine Gravity and Ghosts
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• A family of solutions to the inverse problem in gravitation: building a theory around a metric
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism